Solving SCS for bounded length strings in fewer than 2n steps - Golovnev, Alexander; Kulikov, Alexander S.; Mihajlin, Ivan (Information processing letters, 2014)
It is still not known whether a shortest common superstring (SCS) of n input strings can be found faster than in O⁎(2n) time (O⁎(⋅) suppresses polynomial factors of the input length). In this short note, we show that for any constant r, SCS for strings of length at most r can be solved in time O⁎(2(1−c(r))n) where c(r)=(1+2r2)−1. For this, we introduce so-called hierarchical graphs that allow us to reduce SCS on strings of length at most r to the directed rural postman problem on a graph with at most k=(1−c(r))n weakly connected components. One can then use a recent O⁎(2k) time algorithm by Gutin, Wahlström, and Yeo. •We study the shortest common superstring problem on string of length r (r-SCS).•We introduce hierarchical graphs to reduce the r-SCS problem to the directed rural postman problem (DRPP).•We bound the number of weakly connected components in hierarchical graphs and call recent algorithm by Gutin et al.•The main result is a randomized 2n(1−Ω(r−2))-time algorithm for r-SCS.